Subgroups — D₅×#4149 #13107837

Order 1600.

1962 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11717522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#4149	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	#11717485	C₂	1	2	yes	maximal, complemented
5	D₅×#713	C₂	1	2	yes	maximal, complemented
6	#11717479	C₂	1	6	yes	maximal, complemented
7	D₄×D₅²	C₂	1	6	yes	maximal, complemented
8	#11717473	C₂	1	3	yes	maximal, complemented
9	#11717472	C₂	1	3	yes	maximal, complemented
10	D₅×#709	C₂	1	3	yes	maximal, complemented
11	C₂×D₅×D₂₀	C₂	1	3	yes	maximal, complemented
12	C₂²×D₅²	C₂²	1	6	yes	complemented
13	C₅²×#41	C₂²	1	1	yes	characteristic, complemented
14	#87904	C₂²	1	2	yes	complemented
15	D₄×C₅⋊D₅	C₂²	1	6	yes	complemented
16	#87900	C₂²	1	3	yes	complemented
17	C₂×C₄⋊(C₅⋊D₅)	C₂²	1	3	yes	complemented
18	C₅×#713	C₂²	1	2	yes	complemented
19	C₅×#713	C₂²	1	1	yes	characteristic, complemented
20	C₅×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
21	C₅×#711	C₂²	1	3	yes	complemented
22	C₅×D₄×D₅	C₂²	1	3	yes	complemented
23	C₅×D₄×D₅	C₂²	1	6	yes	complemented
24	C₅×#709	C₂²	1	3	yes	complemented
25	C₅×#709	C₂²	1	3	yes	complemented
26	C₂×C₅×D₂₀	C₂²	1	3	yes	complemented
27	C₂×C₄×C₅×D₅	C₂²	1	3	yes	complemented
28	#87886	C₂²	1	12	yes	complemented
29	D₅×C₂²⋊D₅	C₂²	1	6	yes	complemented
30	D₅×C₂²⋊D₅	C₂²	1	12	yes	complemented
31	C₂×#6038	C₂²	1	6	yes	complemented
32	#87879	C₂²	1	6	yes	complemented
33	#87877	C₂²	1	6	yes	complemented
34	D₅×D₂₀	C₂²	1	3	yes	complemented
35	D₅×D₂₀	C₂²	1	6	yes	complemented
36	D₅×D₂₀	C₂²	1	6	yes	complemented
37	D₅×D₂₀	C₂²	1	6	yes	complemented
38	D₅×D₂₀	C₂²	1	6	yes	complemented
39	C₄×D₅²	C₂²	1	6	yes	complemented
40	#87874	C₂²	1	3	yes	complemented
41	#87874	C₂²	1	6	yes	complemented
42	#87873	C₂²	1	6	yes	complemented
43	#87871	C₂²	1	6	yes	complemented
44	#87870	C₂²	1	3	yes	complemented
45	D₅×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
46	D₅×H(5,𝔽₂)	—	5	1	no	maximal
47	C₂×#4149	—	5	1	no	maximal
48	C₂²×C₅⋊D₅	C₂³	1	6	yes	complemented
49	C₂²×C₅×D₅	C₂³	1	3	yes	—
50	C₂²×C₅×D₅	C₂³	1	6	yes	complemented
51	C₂×D₅²	—	4	12	no	—
52	C₂×D₅²	C₂³	1	6	yes	—
53	C₂×D₅²	C₂³	1	12	yes	complemented
54	C₅²×Q₈	C₂³	1	1	yes	characteristic, complemented
55	C₅²×D₄	C₂³	1	3	yes	complemented
56	C₂×C₄×C₅²	C₂³	1	3	yes	complemented
57	C₂²⋊(C₅⋊D₅)	C₂³	1	6	yes	complemented
58	C₄⋊(C₅⋊D₅)	C₂³	1	3	yes	complemented
59	C₄⋊(C₅⋊D₅)	C₂³	1	6	yes	complemented
60	C₄×C₅⋊D₅	C₂³	1	6	yes	complemented
61	#6045	C₂³	1	1	yes	characteristic, complemented
62	C₅×C₂²⋊D₅	C₂³	1	6	yes	complemented
63	C₅×C₂²⋊D₅	C₂³	1	6	yes	complemented
64	C₂×C₅×Dic₅	C₂³	1	3	yes	complemented
65	C₅×D₂₀	C₂³	1	3	yes	complemented
66	C₅×D₂₀	C₂³	1	6	yes	complemented
67	C₅×D₂₀	C₂³	1	3	yes	complemented
68	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
69	C₄×C₅×D₅	C₂³	1	3	yes	—
70	C₄×C₅×D₅	C₂³	1	3	yes	complemented
71	C₄×C₅×D₅	C₂³	1	3	yes	complemented
72	C₄×C₅×D₅	C₂³	1	6	yes	complemented
73	C₅×Dic₁₀	C₂³	1	1	yes	characteristic, complemented
74	C₅×Dic₁₀	C₂³	1	3	yes	complemented
75	#6039	C₂³	1	2	yes	complemented
76	#6038	C₂³	1	12	yes	complemented
77	#6038	C₂³	1	6	yes	complemented
78	#6038	C₂³	1	6	yes	complemented
79	#6037	C₂³	1	6	yes	complemented
80	#6036	C₂³	1	6	yes	complemented
81	D₅×Dic₅	C₂³	1	2	yes	—
82	D₅×Dic₅	C₂³	1	6	yes	complemented
83	C₅×H(5,𝔽₂)	—	5	1	no	—
84	C₂×C₅×#41	—	5	1	no	—
85	#4149	—	5	1	no	—
86	#4149	—	5	1	no	—
87	#4149	—	5	2	no	—
88	#4149	—	5	2	no	—
89	#4149	—	5	6	no	—
90	#4149	—	5	3	no	—
91	#4149	—	5	3	no	—
92	#4149	—	5	3	no	—
93	#4149	—	10	2	no	—
94	#4149	D₅	1	1	yes	characteristic, direct product factor
95	D₅×#41	—	5	2	no	—
96	D₅×#41	—	5	3	no	—
97	D₅×#41	D₅	1	1	yes	characteristic, complemented
98	C₂×#713	—	5	2	no	—
99	#4144	—	5	6	no	—
100	#4144	—	5	3	no	—
101	C₂×D₄×D₅	—	5	6	no	—
102	C₂×D₄×D₅	—	5	6	no	—
103	C₂×D₄×D₅	—	5	3	no	—
104	C₂×#709	—	5	3	no	—
105	C₂²×D₂₀	—	5	3	no	—
106	C₂²×C₅²	C₂⁴	1	3	yes	—
107	C₂×C₅⋊D₅	—	4	6	no	—
108	C₂×C₅⋊D₅	C₂⁴	1	6	yes	—
109	C₂×C₅×D₅	—	2	6	no	—
110	C₂×C₅×D₅	—	4	6	no	—
111	C₂×C₅×D₅	C₂⁴	1	6	yes	—
112	C₂×C₅×D₅	C₂⁴	1	3	yes	—
113	C₂×C₅×D₅	C₂⁴	1	1	yes	characteristic
114	D₅²	—	2	12	no	—
115	D₅²	—	4	12	no	—
116	C₄×C₅²	C₂⁴	1	1	yes	characteristic
117	C₄×C₅²	C₂⁴	1	3	yes	—
118	#1039	C₂⁴	1	2	yes	—
119	C₅×Dic₅	C₂⁴	1	2	yes	—
120	C₅×Dic₅	C₂⁴	1	3	yes	—
121	C₅×Dic₅	C₂⁴	1	1	yes	characteristic
122	C₂³×D₅	—	5	6	no	—
123	C₂³×D₅	—	5	6	no	—
124	C₅×#41	—	2	2	no	—
125	C₅×#41	—	5	2	no	—
126	C₅×#41	—	5	1	no	—
127	C₅×#41	—	5	3	no	—
128	C₅×#41	—	5	3	no	—
129	C₅×#41	—	5	3	no	—
130	C₅×#41	C₂×D₅	1	1	yes	characteristic, complemented
131	C₅×#41	C₂×D₅	1	1	yes	characteristic, complemented
132	C₂×C₅×Q₈	—	5	1	no	—
133	C₂×C₅×D₄	—	5	3	no	—
134	C₂×C₅×D₄	—	5	6	no	—
135	C₂×C₅×D₄	—	5	3	no	—
136	C₂²×C₄×C₅	—	5	3	no	—
137	C₂×C₂²⋊D₅	—	5	6	no	—
138	C₂×C₂²⋊D₅	—	5	12	no	—
139	C₂×C₂²⋊D₅	—	5	6	no	—
140	#713	—	5	2	no	—
141	#713	—	5	2	no	—
142	#713	—	5	6	no	—
143	#713	—	5	6	no	—
144	#713	—	5	3	no	—
145	#713	—	10	4	no	—
146	#713	C₂×D₅	1	2	yes	complemented
147	#713	C₂×D₅	1	1	yes	characteristic, complemented
148	Q₈×D₅	—	5	1	no	—
149	Q₈×D₅	C₂×D₅	1	1	yes	characteristic, complemented
150	#711	—	5	6	no	—
151	#711	—	5	3	no	—
152	#711	—	5	6	no	—
153	#711	C₂×D₅	1	3	yes	complemented
154	D₄×D₅	—	5	6	no	—
155	D₄×D₅	—	5	12	no	—
156	D₄×D₅	—	5	6	no	—
157	D₄×D₅	—	5	6	no	—
158	D₄×D₅	—	5	12	no	—
159	D₄×D₅	—	5	12	no	—
160	D₄×D₅	—	5	6	no	—
161	D₄×D₅	—	5	6	no	—
162	D₄×D₅	—	5	6	no	—
163	D₄×D₅	—	5	3	no	—
164	D₄×D₅	—	5	6	no	—
165	D₄×D₅	—	5	6	no	—
166	D₄×D₅	—	5	6	no	—
167	D₄×D₅	—	10	12	no	—
168	D₄×D₅	C₂×D₅	1	3	yes	complemented
169	D₄×D₅	C₂×D₅	1	6	yes	complemented
170	#709	—	5	3	no	—
171	#709	—	5	3	no	—
172	#709	—	5	6	no	—
173	#709	—	5	3	no	—
174	#709	—	5	6	no	—
175	#709	—	5	6	no	—
176	#709	—	5	3	no	—
177	#709	—	5	6	no	—
178	#709	—	10	6	no	—
179	#709	C₂×D₅	1	3	yes	complemented
180	#709	C₂×D₅	1	3	yes	complemented
181	C₂×D₂₀	—	5	6	no	—
182	C₂×D₂₀	—	5	3	no	—
183	C₂×D₂₀	—	5	3	no	—
184	C₂×D₂₀	—	5	3	no	—
185	C₂×D₂₀	—	5	6	no	—
186	C₂×D₂₀	—	5	6	no	—
187	C₂×D₂₀	—	5	6	no	—
188	C₂×D₂₀	—	5	6	no	—
189	C₂×D₂₀	—	10	6	no	—
190	C₂×D₂₀	C₂×D₅	1	3	yes	complemented
191	C₂×C₄×D₅	—	5	6	no	—
192	C₂×C₄×D₅	—	5	6	no	—
193	C₂×C₄×D₅	C₂×D₅	1	3	yes	complemented
194	C₂×Dic₁₀	—	5	1	no	—
195	C₂×H(5,𝔽₂)	—	25	1	no	Sylow
196	C₂×C₅²	—	2	3	no	—
197	C₂×C₅²	C₂⁵	1	1	yes	characteristic
198	C₅⋊D₅	—	2	6	no	—
199	C₅×D₅	—	2	6	no	—
200	C₅×D₅	—	2	3	no	—
201	C₅×D₅	H(5,𝔽₂)	1	2	yes	complemented
202	C₂³×C₅	—	5	3	no	—
203	C₂³×C₅	—	5	6	no	—
204	C₂²×D₅	—	5	6	no	—
205	C₂²×D₅	—	5	6	no	—
206	C₂²×D₅	—	5	6	no	—
207	C₂²×D₅	—	5	6	no	—
208	C₂²×D₅	—	5	12	no	—
209	C₂²×D₅	—	5	12	no	—
210	C₂²×D₅	—	10	12	no	—
211	C₂²×D₅	—	20	12	no	—
212	C₂²×D₅	—	20	12	no	—
213	C₂²×D₅	C₂²×D₅	1	3	yes	—
214	C₂²×D₅	C₂²×D₅	1	6	yes	complemented
215	C₅×Q₈	—	2	2	no	—
216	C₅×Q₈	—	5	1	no	—
217	C₅×Q₈	—	5	3	no	—
218	C₅×Q₈	C₂²×D₅	1	1	yes	characteristic, complemented
219	C₅×Q₈	C₂²×D₅	1	1	yes	characteristic, complemented
220	C₅×D₄	—	2	6	no	—
221	C₅×D₄	—	5	6	no	—
222	C₅×D₄	—	5	6	no	—
223	C₅×D₄	—	5	3	no	—
224	C₅×D₄	—	5	3	no	—
225	C₅×D₄	—	5	6	no	—
226	C₅×D₄	C₂²×D₅	1	3	yes	complemented
227	C₅×D₄	C₂²×D₅	1	3	yes	complemented
228	C₂×C₄×C₅	—	2	6	no	—
229	C₂×C₄×C₅	—	5	3	no	—
230	C₂×C₄×C₅	—	5	1	no	—
231	C₂×C₄×C₅	—	5	3	no	—
232	C₂×C₄×C₅	—	5	6	no	—
233	C₂×C₄×C₅	—	5	3	no	—
234	C₂×C₄×C₅	—	5	3	no	—
235	C₂×C₄×C₅	C₂²×D₅	1	3	yes	complemented
236	C₂×C₄×C₅	C₂²×D₅	1	3	yes	complemented
237	C₂²⋊D₅	—	5	6	no	—
238	C₂²⋊D₅	—	5	6	no	—
239	C₂²⋊D₅	—	5	6	no	—
240	C₂²⋊D₅	—	5	6	no	—
241	C₂²⋊D₅	—	5	6	no	—
242	C₂²⋊D₅	—	5	6	no	—
243	C₂²⋊D₅	—	5	12	no	—
244	C₂²⋊D₅	—	10	12	no	—
245	C₂²⋊D₅	C₂²×D₅	1	6	yes	complemented
246	C₂²⋊D₅	C₂²×D₅	1	6	yes	complemented
247	C₂×Dic₅	—	5	2	no	—
248	C₂×Dic₅	—	5	6	no	—
249	C₂×Dic₅	C₂²×D₅	1	3	yes	complemented
250	D₂₀	—	5	6	no	—
251	D₂₀	—	5	12	no	—
252	D₂₀	—	5	6	no	—
253	D₂₀	—	5	3	no	—
254	D₂₀	—	5	6	no	—
255	D₂₀	—	5	3	no	—
256	D₂₀	—	5	6	no	—
257	D₂₀	—	10	6	no	—
258	D₂₀	—	10	12	no	—
259	D₂₀	C₂²×D₅	1	3	yes	complemented
260	D₂₀	C₂²×D₅	1	6	yes	complemented
261	D₂₀	C₂²×D₅	1	3	yes	complemented
262	C₄×D₅	—	5	2	no	—
263	C₄×D₅	—	5	6	no	—
264	C₄×D₅	—	5	6	no	—
265	C₄×D₅	—	5	6	no	—
266	C₄×D₅	—	5	6	no	—
267	C₄×D₅	—	5	6	no	—
268	C₄×D₅	—	10	12	no	—
269	C₄×D₅	C₂²×D₅	1	3	yes	—
270	C₄×D₅	C₂²×D₅	1	1	yes	characteristic
271	C₄×D₅	C₂²×D₅	1	6	yes	complemented
272	C₄×D₅	C₂²×D₅	1	3	yes	complemented
273	C₄×D₅	C₂²×D₅	1	3	yes	complemented
274	Dic₁₀	—	5	1	no	—
275	Dic₁₀	—	5	1	no	—
276	Dic₁₀	—	5	2	no	—
277	Dic₁₀	—	5	2	no	—
278	Dic₁₀	—	10	2	no	—
279	Dic₁₀	C₂²×D₅	1	1	yes	characteristic, complemented
280	Dic₁₀	C₂²×D₅	1	3	yes	complemented
281	H(5,𝔽₂)	—	5	1	no	—
282	H(5,𝔽₂)	—	25	6	no	—
283	H(5,𝔽₂)	—	25	3	no	—
284	H(5,𝔽₂)	—	25	2	no	—
285	H(5,𝔽₂)	—	25	3	no	—
286	H(5,𝔽₂)	—	25	1	no	—
287	C₂×#41	—	5	1	no	—
288	C₂×#41	—	25	3	no	—
289	C₂×#41	—	25	2	no	—
290	C₂²×D₄	—	25	3	no	—
291	C₂²×D₄	—	25	6	no	—
292	C₅²	C₂×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
293	C₂²×C₅	—	2	6	no	—
294	C₂²×C₅	—	5	1	no	—
295	C₂²×C₅	—	5	6	no	—
296	C₂²×C₅	—	5	3	no	—
297	C₂²×C₅	—	10	6	no	—
298	C₂²×C₅	—	20	6	no	—
299	C₂²×C₅	C₂³×D₅	1	3	yes	—
300	C₂²×C₅	C₂³×D₅	1	3	yes	—
301	C₂×D₅	—	2	6	no	—
302	C₂×D₅	—	4	6	no	—
303	C₂×D₅	—	5	6	no	—
304	C₂×D₅	—	5	6	no	—
305	C₂×D₅	—	10	12	no	—
306	C₂×D₅	—	10	12	no	—
307	C₂×D₅	—	10	12	no	—
308	C₂×D₅	—	20	12	no	—
309	C₂×D₅	—	20	12	no	—
310	C₂×D₅	—	20	6	no	—
311	C₂×D₅	—	20	6	no	—
312	C₂×D₅	—	40	12	no	—
313	C₂×D₅	C₂³×D₅	1	6	yes	—
314	C₂×D₅	C₂³×D₅	1	3	yes	—
315	C₂×D₅	C₂³×D₅	1	1	yes	characteristic
316	C₄×C₅	—	2	2	no	—
317	C₄×C₅	—	2	6	no	—
318	C₄×C₅	—	5	1	no	—
319	C₄×C₅	—	5	2	no	—
320	C₄×C₅	—	5	3	no	—
321	C₄×C₅	C₂³×D₅	1	1	yes	characteristic
322	C₄×C₅	C₂³×D₅	1	1	yes	characteristic
323	C₄×C₅	C₂³×D₅	1	3	yes	—
324	C₄×C₅	C₂³×D₅	1	3	yes	—
325	Dic₅	—	5	2	no	—
326	Dic₅	—	5	2	no	—
327	Dic₅	—	10	4	no	—
328	Dic₅	C₂³×D₅	1	1	yes	characteristic
329	Dic₅	C₂³×D₅	1	2	yes	—
330	Dic₅	C₂³×D₅	1	3	yes	—
331	C₂⁴	—	25	6	no	—
332	#41	—	5	1	no	—
333	#41	—	5	2	no	—
334	#41	—	5	3	no	—
335	#41	—	5	3	no	—
336	#41	—	5	3	no	—
337	#41	—	25	6	no	—
338	#41	—	25	6	no	—
339	#41	—	25	3	no	—
340	#41	—	25	3	no	—
341	#41	—	25	6	no	—
342	#41	—	25	6	no	—
343	#41	—	25	2	no	—
344	#41	—	25	3	no	—
345	#41	D₅²	1	1	yes	characteristic, complemented
346	C₂×Q₈	—	5	1	no	—
347	C₂×Q₈	—	25	1	no	—
348	C₂×D₄	—	5	3	no	—
349	C₂×D₄	—	5	6	no	—
350	C₂×D₄	—	5	3	no	—
351	C₂×D₄	—	25	3	no	—
352	C₂×D₄	—	25	6	no	—
353	C₂×D₄	—	25	6	no	—
354	C₂×D₄	—	25	6	no	—
355	C₂×D₄	—	25	6	no	—
356	C₂×D₄	—	25	6	no	—
357	C₂×D₄	—	25	12	no	—
358	C₂×D₄	—	25	6	no	—
359	C₂×D₄	—	25	6	no	—
360	C₂×D₄	—	25	12	no	—
361	C₂×D₄	—	25	6	no	—
362	C₂×D₄	—	25	3	no	—
363	C₂²×C₄	—	5	3	no	—
364	C₂²×C₄	—	25	6	no	—
365	C₂×C₅	—	2	3	no	—
366	C₂×C₅	—	2	3	no	—
367	C₂×C₅	—	2	2	no	—
368	C₂×C₅	—	4	6	no	—
369	C₂×C₅	—	5	2	no	—
370	C₂×C₅	—	10	6	no	—
371	C₂×C₅	—	10	3	no	—
372	C₂×C₅	C₂⁴×D₅	1	1	yes	characteristic
373	C₂×C₅	C₂⁴×D₅	1	1	yes	characteristic
374	D₅	—	2	3	no	—
375	D₅	—	2	6	no	—
376	D₅	—	10	6	no	—
377	D₅	—	10	6	no	—
378	D₅	—	20	12	no	—
379	D₅	#4149	1	2	yes	direct product factor
380	C₂³	—	5	3	no	—
381	C₂³	—	5	6	no	—
382	C₂³	—	25	6	no	—
383	C₂³	—	25	12	no	—
384	C₂³	—	25	6	no	—
385	C₂³	—	100	12	no	—
386	Q₈	—	5	3	no	—
387	Q₈	—	5	1	no	—
388	Q₈	—	25	2	no	—
389	Q₈	—	25	1	no	—
390	Q₈	C₂×D₅²	1	1	yes	characteristic, complemented
391	D₄	—	5	6	no	—
392	D₄	—	5	6	no	—
393	D₄	—	5	6	no	—
394	D₄	—	5	3	no	—
395	D₄	—	5	3	no	—
396	D₄	—	25	6	no	—
397	D₄	—	25	6	no	—
398	D₄	—	25	12	no	—
399	D₄	—	25	6	no	—
400	D₄	—	25	6	no	—
401	D₄	—	25	6	no	—
402	D₄	—	25	3	no	—
403	D₄	C₂×D₅²	1	3	yes	complemented
404	C₂×C₄	—	5	3	no	—
405	C₂×C₄	—	5	1	no	—
406	C₂×C₄	—	5	3	no	—
407	C₂×C₄	—	5	3	no	—
408	C₂×C₄	—	5	3	no	—
409	C₂×C₄	—	5	6	no	—
410	C₂×C₄	—	25	6	no	—
411	C₂×C₄	—	25	2	no	—
412	C₂×C₄	—	25	6	no	—
413	C₂×C₄	—	25	6	no	—
414	C₂×C₄	C₂×D₅²	1	3	yes	complemented
415	C₅	—	2	2	no	—
416	C₅	C₂×#4149	1	1	yes	characteristic, complemented
417	C₅	D₅×H(5,𝔽₂)	1	1	yes	characteristic, complemented
418	C₂²	—	5	1	no	—
419	C₂²	—	5	3	no	—
420	C₂²	—	5	6	no	—
421	C₂²	—	10	6	no	—
422	C₂²	—	20	6	no	—
423	C₂²	—	25	6	no	—
424	C₂²	—	50	12	no	—
425	C₂²	—	100	6	no	—
426	C₂²	—	100	12	no	—
427	C₂²	C₂²×D₅²	1	3	yes	—
428	C₄	—	5	1	no	—
429	C₄	—	5	2	no	—
430	C₄	—	5	3	no	—
431	C₄	—	25	2	no	—
432	C₄	C₂²×D₅²	1	3	yes	—
433	C₄	C₂²×D₅²	1	1	yes	characteristic
434	C₂	—	2	3	no	—
435	C₂	—	5	2	no	—
436	C₂	—	10	3	no	—
437	C₂	—	10	6	no	—
438	C₂	—	50	6	no	—
439	C₂	C₂³×D₅²	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×D₅²
commutator, socle, cosocle	C₂×C₅²	C₂⁵
Fitting	C₅²×#41	C₂²
hypercenter	#41	D₅²
hypocenter	C₅²	C₂×H(5,𝔽₂)
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ #41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #11717522	C₂	semidirect
2. C₅×#4149	C₂	semidirect
3. C₅×D₅×#41	C₂	semidirect
4. #11717485	C₂	semidirect
5. D₅×#713	C₂	semidirect
6. #11717479	C₂	semidirect
7. D₄×D₅²	C₂	semidirect
8. #11717473	C₂	semidirect
9. #11717472	C₂	semidirect
10. D₅×#709	C₂	semidirect
11. C₂×D₅×D₂₀	C₂	semidirect
12. C₂²×D₅²	C₂²	semidirect
13. C₅²×#41	C₂²	semidirect
14. #87904	C₂²	semidirect
15. D₄×C₅⋊D₅	C₂²	semidirect
16. #87900	C₂²	semidirect
17. C₂×C₄⋊(C₅⋊D₅)	C₂²	semidirect
18. C₅×#713	C₂²	semidirect
19. C₅×#713	C₂²	semidirect
20. C₅×Q₈×D₅	C₂²	semidirect
21. C₅×#711	C₂²	semidirect
22. C₅×D₄×D₅	C₂²	semidirect
23. C₅×D₄×D₅	C₂²	semidirect
24. C₅×#709	C₂²	semidirect
25. C₅×#709	C₂²	semidirect
26. C₂×C₅×D₂₀	C₂²	semidirect
27. C₂×C₄×C₅×D₅	C₂²	semidirect
28. #87886	C₂²	semidirect
29. D₅×C₂²⋊D₅	C₂²	semidirect
30. D₅×C₂²⋊D₅	C₂²	semidirect
31. C₂×#6038	C₂²	semidirect
32. #87879	C₂²	semidirect
33. #87877	C₂²	semidirect
34. D₅×D₂₀	C₂²	semidirect
35. D₅×D₂₀	C₂²	semidirect
36. D₅×D₂₀	C₂²	semidirect
37. D₅×D₂₀	C₂²	semidirect
38. D₅×D₂₀	C₂²	semidirect
39. C₄×D₅²	C₂²	semidirect
40. #87874	C₂²	semidirect
41. #87874	C₂²	semidirect
42. #87873	C₂²	semidirect
43. #87871	C₂²	semidirect
44. #87870	C₂²	semidirect
45. D₅×Dic₁₀	C₂²	semidirect
48. C₂²×C₅⋊D₅	C₂³	semidirect
50. C₂²×C₅×D₅	C₂³	semidirect
53. C₂×D₅²	C₂³	semidirect
54. C₅²×Q₈	C₂³	semidirect
55. C₅²×D₄	C₂³	semidirect
56. C₂×C₄×C₅²	C₂³	semidirect
57. C₂²⋊(C₅⋊D₅)	C₂³	semidirect
58. C₄⋊(C₅⋊D₅)	C₂³	semidirect
59. C₄⋊(C₅⋊D₅)	C₂³	semidirect
60. C₄×C₅⋊D₅	C₂³	semidirect
61. #6045	C₂³	semidirect
62. C₅×C₂²⋊D₅	C₂³	semidirect
63. C₅×C₂²⋊D₅	C₂³	semidirect
64. C₂×C₅×Dic₅	C₂³	semidirect
65. C₅×D₂₀	C₂³	semidirect
66. C₅×D₂₀	C₂³	semidirect
67. C₅×D₂₀	C₂³	semidirect
70. C₄×C₅×D₅	C₂³	semidirect
71. C₄×C₅×D₅	C₂³	semidirect
72. C₄×C₅×D₅	C₂³	semidirect
73. C₅×Dic₁₀	C₂³	semidirect
74. C₅×Dic₁₀	C₂³	semidirect
75. #6039	C₂³	semidirect
76. #6038	C₂³	semidirect
77. #6038	C₂³	semidirect
78. #6038	C₂³	semidirect
79. #6037	C₂³	semidirect
80. #6036	C₂³	semidirect
82. D₅×Dic₅	C₂³	semidirect
94. #4149	D₅	direct (N × H)
97. D₅×#41	D₅	semidirect
130. C₅×#41	C₂×D₅	semidirect
131. C₅×#41	C₂×D₅	semidirect
146. #713	C₂×D₅	semidirect
147. #713	C₂×D₅	semidirect
149. Q₈×D₅	C₂×D₅	semidirect
153. #711	C₂×D₅	semidirect
168. D₄×D₅	C₂×D₅	semidirect
169. D₄×D₅	C₂×D₅	semidirect
179. #709	C₂×D₅	semidirect
180. #709	C₂×D₅	semidirect
190. C₂×D₂₀	C₂×D₅	semidirect
193. C₂×C₄×D₅	C₂×D₅	semidirect
201. C₅×D₅	H(5,𝔽₂)	semidirect
214. C₂²×D₅	C₂²×D₅	semidirect
218. C₅×Q₈	C₂²×D₅	semidirect
219. C₅×Q₈	C₂²×D₅	semidirect
226. C₅×D₄	C₂²×D₅	semidirect
227. C₅×D₄	C₂²×D₅	semidirect
235. C₂×C₄×C₅	C₂²×D₅	semidirect
236. C₂×C₄×C₅	C₂²×D₅	semidirect
245. C₂²⋊D₅	C₂²×D₅	semidirect
246. C₂²⋊D₅	C₂²×D₅	semidirect
249. C₂×Dic₅	C₂²×D₅	semidirect
259. D₂₀	C₂²×D₅	semidirect
260. D₂₀	C₂²×D₅	semidirect
261. D₂₀	C₂²×D₅	semidirect
271. C₄×D₅	C₂²×D₅	semidirect
272. C₄×D₅	C₂²×D₅	semidirect
273. C₄×D₅	C₂²×D₅	semidirect
279. Dic₁₀	C₂²×D₅	semidirect
280. Dic₁₀	C₂²×D₅	semidirect
292. C₅²	C₂×H(5,𝔽₂)	semidirect
345. #41	D₅²	semidirect
379. D₅	#4149	direct (N × H)
390. Q₈	C₂×D₅²	semidirect
403. D₄	C₂×D₅²	semidirect
414. C₂×C₄	C₂×D₅²	semidirect
416. C₅	C₂×#4149	semidirect
417. C₅	D₅×H(5,𝔽₂)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#11717522	2
C₅×#4149	2
C₅×D₅×#41	2
#11717485	2
D₅×#713	2
#11717479	2
D₄×D₅²	2
#11717473	2
#11717472	2
D₅×#709	2
C₂×D₅×D₂₀	2
D₅×H(5,𝔽₂)	5
C₂×#4149	5

Subgroups — D5×#4149 #13107837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#4149 #13107837